Subducted slabs are stagnant in the mantle transition

Subducted slabs are stagnant in the mantle transition zone, and then collapsed into the lower mantle (from Fukao et al. 1992; 2001)

4. Birch’s Law • Birch’s Law – Birch (1961 b) VPと密度の関係式 “As a provisional hypothesis, it will be postulated that the velocity-density relations, as expressed above, hold for all changes of density in the Earth’s mantle, however produced. ” 圧縮による密度変化や化学組成が変わる（ただし平均原子量は不変）ことによる密度変化は弾性波速度へ同じ変化をもたらす平均原子量が同じ異なる物質のBirchの関係式の傾き最密構造（例：Corundum, rock salt, perovskite）では 3以下それ以外（例：Olivine, quartz）では傾き4以上

The outer core density: lower by 7 - 10 % than that of pure iron (Anderson and Issak, 2002; Shanker et al. , 2004). High solubility of O and Si in molten iron may explain the density deficit of the core. 8

After Fiquet et al. (2004) Fe Theory (Steinle-Neumann Et al. (2001) NRIXS (Mao et al. (2001) at 300 K IXS Fiquet et al. (2001) at 300 K PREM inner Shock core Brown and Mc. Qween (1986) at 3000 -6000 K Discrepancy: IXS　Ｘ線非弾性散乱 and Shock vs NRIXS 核共鳴Ｘ線非弾性散乱 Temperature effect on Birch law ? 　温度依存性 40

4. Birch’s Law • 核物質のVP 40. 0 42. 0 核物質のVPはBirch’s lawに従う 44. 9 55. 8 35. 9 49. 9 Badro et al. (2007) x: 鉄の核中での体積比率 44. 0

BL 35 XU Optics: Baron et al. (2000) Si (9, 9, 9) and Si(11, 11) Instrument configuration X-ray beam size 70 x 70 μm 2 41

670 km Bulk sound velocity Vf (km/sec) 400 km 670 km Mg 3 Al 2 Si 3 O 12 220 km P Mg 2 Si. O 4 T spinel garnet Fe 3 Al 2 Si 3 O 12 olivine Fe 2 Si. O 4 Density g/cm 3 温度、圧力、組成、相転移依存性」

復習 670 km Bulk sound velocity Vf (km/sec) 400 km 670 km Mg 3 Al 2 Si 3 O 12 220 km P Mg 2 Si. O 4 T spinel garnet Fe 3 Al 2 Si 3 O 12 olivine Fe 2 Si. O 4 Density g/cm 3 温度、圧力、組成、相転移依存性」

　 ln. Vb = (dc-1)/2 = constant = 1. 5~2. 5, where dc~4 lnr P の証明 ln Vb=(ln. Ks-lnr)/2 ゆえに ln. Ks -1 lnr ln. Vb = lnr P = (dc-1) ここで dc：Anderson-Gruneisen Constant 温度によらず一定 dc = ln. Ks lnr =P ln. Ks = ln. V P a ln. Ks T = constant P